SOLUTION: A normal distribution has a mean of 85.5 and a standard deviation of 4.81. Find the data value corresponding to the value of z given. z = −3.41 (Enter your answer to four deci

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Question 1186922: A normal distribution has a mean of 85.5 and a standard deviation of 4.81. Find the data value corresponding to the value of z given. z = −3.41
(Enter your answer to four decimal places.)

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
z = (x - m) / s

z is the z-score
x is the raw score
m is the mean
s is the standard deviation

in your problem:

m = 85.5
s = 4.81
z = -3.41

use the z-score formula to find the raw score.

z = (x - m) / s becomes -3.41 = (x - 85.5) / 4.81
multiply both sides of the equation by 4.81 to get:
-3.41 * 4.81 = x - 85.5
add 85.5 to both sides of the equation to get:
-3.41 * 4.81 + 85.5 = x
solve for x to get:
x = 69.0979

that's your raw score.

if the raw score is equivalent to the z-score, you should be able to use a z-score calculator to determine that they both have the same area to the left of them.

i used the z-score calculator at https://www.statskingdom.com/normal.html to do that.

for the z-score, i set the mean to 0 and the standard deviation to 1 and then looked for the area to the left of the z-score of -3.41.

these are the results.

for the raw score, i set the mean to 85.5 and the standard deviation to 4.81 and then looked for the area to the left of the raw score of 69.0979

these are the results.

in these displays, you can see that:

p(x <= -3.41) and p(x <= 69.0979) are the same.

the data value you are looking for is the raw score.

your solution is 69.0979.